We propose an end-to-end speech enhancement method with trainable time-frequency~(T-F) transform based on invertible deep neural network~(DNN). The resent development of speech enhancement is brought by using DNN. The ordinary DNN-based speech enhancement employs T-F transform, typically the short-time Fourier transform~(STFT), and estimates a T-F mask using DNN. On the other hand, some methods have considered end-to-end networks which directly estimate the enhanced signals without T-F transform. While end-to-end methods have shown promising results, they are black boxes and hard to understand. Therefore, some end-to-end methods used a DNN to learn the linear T-F transform which is much easier to understand. However, the learned transform may not have a property important for ordinary signal processing. In this paper, as the important property of the T-F transform, perfect reconstruction is considered. An invertible nonlinear T-F transform is constructed by DNNs and learned from data so that the obtained transform is perfectly reconstructing filterbank.